Optimal. Leaf size=22 \[ x \text {PolyLog}\left (-\frac {1}{2},a x\right )-\text {Int}\left (\text {PolyLog}\left (-\frac {1}{2},a x\right ),x\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.00, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps
used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {}
\begin {gather*} \int \text {Li}_{-\frac {3}{2}}(a x) \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
Rubi steps
\begin {align*} \int \text {Li}_{-\frac {3}{2}}(a x) \, dx &=x \text {Li}_{-\frac {1}{2}}(a x)-\int \text {Li}_{-\frac {1}{2}}(a x) \, dx\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.01, size = 0, normalized size = 0.00 \begin {gather*} \int \text {PolyLog}\left (-\frac {3}{2},a x\right ) \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.02, size = 0, normalized size = 0.00 \[\int \polylog \left (-\frac {3}{2}, a x \right )\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \operatorname {Li}_{- \frac {3}{2}}\left (a x\right )\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [A]
time = 0.00, size = -1, normalized size = -0.05 \begin {gather*} \int \mathrm {polylog}\left (-\frac {3}{2},a\,x\right ) \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________